Optimal Impulsive Rendezvous for Approaching Geostationary Earth Orbit Targets with Terminal Configuration Constraints

Abstract

This paper explores multi-impulse trajectory design for approaching Geostationary Earth Orbit (GEO) targets, emphasizing the attainment of a 2:1 elliptical relative orbit for close inspection. The intricate optimization challenge includes dynamic and terminal constraints, as well as total mission duration limitations. Critical variables like transfer duration, impulse count, timing, and entry point are optimized using genetic algorithms to minimize velocity increment requirements. These optimal values are influenced by uncertain terminal states constrained by the 2:1 circling orbit. To address these complexities, the paper leverages a linear state transition matrix from relative orbital dynamics to formulate a multi-impulse optimization model. Additionally, a differential correction-based iterative approach mitigates nonlinear dynamics’ impact on terminal rendezvous errors. Through theoretical analysis and simulations, the study elucidates variations in optimization criteria, particularly in GEO missions with multiple impulses, and identifies optimal entry points for different impulse counts. The proposed models and methodologies offer theoretical insights for future GEO orbit approaching missions and potential applications in various space maneuver tasks.